Learning representations of sets w/ neural networks

Most research in machine learning deals with inputs that are single vectors (like a photo), or sequences of vectors (like a video). An underexplored setting is dealing with unordered sets of vectors (like a collection of photos of a person). In my PhD I will develop techniques for dealing with sets using neural networks. One interesting problem in this space is predicting whether a given element belongs to a set or not. This could have applications to information retrieval, speaker/face verification and recommendation systems.